integral of sec^{13}(x)

解答

\int sec^{13} (x) d x

\frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} (\frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))) + C

求解步骤

\int sec^{13} (x) d x

使用降次积分法

= \frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} \cdot \int sec^{11} (x) d x

\int sec^{11} (x) d x = \frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))

= \frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} (\frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣)))))

解答补常数

= \frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} (\frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))) + C

f (x) = sinh (2 x)

\int_{0}^{l n (2)} e^{x + 2 y} d x

\frac{\partial}{\partial x} (2 x \cdot e^{x y})

\frac{\partial}{\partial x} (x^{2} z + 3 z^{2} x + 6 (x + z))

\frac{d}{d x} (2 x^{6} - 8 x^{5} + 10 x^{4} - 10 x^{2} + 8 x - 2)